Problem: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{y^2 - 14y + 45}{y^2 - 9y}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 - 14y + 45}{y^2 - 9y} = \dfrac{(y - 5)(y - 9)}{(y)(y - 9)} $ Notice that the term $(y - 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y - 9)$ gives: $p = \dfrac{y - 5}{y}$ Since we divided by $(y - 9)$, $y \neq 9$. $p = \dfrac{y - 5}{y}; \space y \neq 9$